# ps5 - UCSB Fall 2007 ECE 130A Problem Set 5 Assigned...

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UCSB Fall 2007 ECE 130A: Problem Set 5 Assigned: Tuesday, November 6 Due: Tuesday, November 13 Reading: 4.1-4.5 Problem 1 Fourier transform computation: 4.21(a),(b),(f) Problem 2 Inverse Fourier transform computation 4.4, 4.5 Problem 3 Fourier transform gives system frequency response: (a) An LTI system has impulse response h ( t ) = 10 I [3 , 5] ( t ). Find and sketch magnitude and phase of the frequency response H ( j 2 πf ) as a function of f . (b) Does the system amplify or attenuate a sinusoid of frequency 22 Hz? By how much? (c) By how much does the system change the phase of the sinusoid? Problem 4: Consider the signal x ( t ) = sinc(4 t ) cos(4 t ). (a) Find and sketch the Fourier transform X ( ) or X ( j 2 πf ) of x ( t ), carefully labeling the axes. (b) Find the energy i -∞ x 2 ( t ) dt . (c) The signal x ( t ) is passed through a ±lter with impulse response h ( t ) = sinc(8 t - 4). Find a time- domain expression for the output y ( t ) = ( x * h )( t ). Problem 5

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ps5 - UCSB Fall 2007 ECE 130A Problem Set 5 Assigned...

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